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 A117737 Numbers such that the (positive) difference between the sum of the digits and the product of the digits is a prime number. 1

%I

%S 20,24,25,27,29,30,33,34,35,37,38,42,43,45,47,49,50,52,53,54,56,57,59,

%T 65,67,70,72,73,74,75,76,78,79,83,87,92,94,95,97,101,102,104,106,110,

%U 111,112,113,114,115,116,117,118,119,120,121,125,126,128,131,133,140

%N Numbers such that the (positive) difference between the sum of the digits and the product of the digits is a prime number.

%H Robert Israel, <a href="/A117737/b117737.txt">Table of n, a(n) for n = 1..10000</a>

%e 97 is in the sequence because the sum of its digits is 16, the product of its digits is 63 and the difference between 16 and 63 is 47, which is a prime.

%p filter:= proc(n) local L;

%p L:= convert(n,base,10);

%p isprime(abs(convert(L,`+`)-convert(L,`*`)))

%p end proc:

%p select(filter, [\$1..1000]); # _Robert Israel_, Jan 22 2019

%t Select[Range[140],PrimeQ[Abs[Plus@@(x=IntegerDigits[#])-Times@@x]]&] (* _Jayanta Basu_, May 18 2013 *)

%o (PARI) sudig(i,suOrmul)= { local(nshft,resul) ; nshft = i ; resul = nshft % 10 ; nshft = nshft \ 10 ; while(nshft>0, if(suOrmul==0, resul += nshft % 10, resul *= nshft % 10 ) ; nshft \= 10 ; ) ; return(resul) ; } { for(n=10,150, summ = sudig(n,0) ; mull = sudig(n,1) ; if( isprime(summ-mull), print1(n,",") ) ; ) ; } \\ _R. J. Mathar_, Apr 21 2006

%Y Cf. A000040.

%K base,nonn

%O 1,1

%A Luc Stevens (lms022(AT)yahoo.com), Apr 14 2006

%E More terms from _R. J. Mathar_, Apr 21 2006

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Last modified December 3 18:14 EST 2020. Contains 338907 sequences. (Running on oeis4.)